estimating the effects of blasting vibrations on …
TRANSCRIPT
University of Kentucky University of Kentucky
UKnowledge UKnowledge
Theses and Dissertations--Mining Engineering Mining Engineering
2017
ESTIMATING THE EFFECTS OF BLASTING VIBRATIONS ON THE ESTIMATING THE EFFECTS OF BLASTING VIBRATIONS ON THE
HIGH-WALL STABILITY HIGH-WALL STABILITY
Abhinav Sharma University of Kentucky, [email protected] Author ORCID Identifier:
https://orcid.org/0000-0001-8732-4750 Digital Object Identifier: https://doi.org/10.13023/ETD.2017.467
Right click to open a feedback form in a new tab to let us know how this document benefits you. Right click to open a feedback form in a new tab to let us know how this document benefits you.
Recommended Citation Recommended Citation Sharma, Abhinav, "ESTIMATING THE EFFECTS OF BLASTING VIBRATIONS ON THE HIGH-WALL STABILITY" (2017). Theses and Dissertations--Mining Engineering. 38. https://uknowledge.uky.edu/mng_etds/38
This Master's Thesis is brought to you for free and open access by the Mining Engineering at UKnowledge. It has been accepted for inclusion in Theses and Dissertations--Mining Engineering by an authorized administrator of UKnowledge. For more information, please contact [email protected].
STUDENT AGREEMENT: STUDENT AGREEMENT:
I represent that my thesis or dissertation and abstract are my original work. Proper attribution
has been given to all outside sources. I understand that I am solely responsible for obtaining
any needed copyright permissions. I have obtained needed written permission statement(s)
from the owner(s) of each third-party copyrighted matter to be included in my work, allowing
electronic distribution (if such use is not permitted by the fair use doctrine) which will be
submitted to UKnowledge as Additional File.
I hereby grant to The University of Kentucky and its agents the irrevocable, non-exclusive, and
royalty-free license to archive and make accessible my work in whole or in part in all forms of
media, now or hereafter known. I agree that the document mentioned above may be made
available immediately for worldwide access unless an embargo applies.
I retain all other ownership rights to the copyright of my work. I also retain the right to use in
future works (such as articles or books) all or part of my work. I understand that I am free to
register the copyright to my work.
REVIEW, APPROVAL AND ACCEPTANCE REVIEW, APPROVAL AND ACCEPTANCE
The document mentioned above has been reviewed and accepted by the student’s advisor, on
behalf of the advisory committee, and by the Director of Graduate Studies (DGS), on behalf of
the program; we verify that this is the final, approved version of the student’s thesis including all
changes required by the advisory committee. The undersigned agree to abide by the statements
above.
Abhinav Sharma, Student
Dr. Jhon Silva-Castro, Major Professor
Dr. Zacharias Agioutantis, Director of Graduate Studies
ESTIMATING THE EFFECTS OF BLASTING VIBRATIONS
ON THE HIGH-WALL STABILITY
THESIS
A thesis submitted in partial fulfillment of the
requirements for the degrees of Master of Science in
Mining Engineering in the College of Engineering
at the University of Kentucky
By
Abhinav Sharma
Lexington, Kentucky
Director: Dr. Jhon Silva-Castro
Assistant Professor of Mining Engineering
Lexington, Kentucky
December 2017
Copyright © Abhinav Sharma 2017
https://orcid.org/0000-0001-8732-4750
ABSTRACT OF THESIS
ESTIMATING THE EFFECTS OF BLASTING VIBRATIONS
ON THE HIGH-WALL STABILITY
The stability of the high-walls is one of the major concerns for open pit mines. Among the
various factors affecting the stability of high-walls, blast vibrations can be an important
one. In general, worldwide the established respective government regulations and industry
standards are used as guidance to determine the maximum recommended levels of the peak
particle velocity and frequency from the blast to avoid any effects on the structures around
the mining project. However, most of the regulations are meant for buildings or houses and
do not concern high-walls.
This thesis investigates the response of high-walls under the effects of vibrations from mine
blasting. In this research, the relationship between the high-wall response, the geometry of
the slope, the frequency and the amplitude, of the ground vibration produced by blasting,
is explored using numerical models in 3DEC. The numerical models were calibrated
initially with data collected using seismographs installed in a surface mine operation and
recording vibrations produced by an underground mine drill and blast operation. Once the
calibration was accomplished, a parametric study was developed to explore the
relationships between various parameters under study and its impact on the stability of
high-walls.
KEYWORDS: High-walls, blasting vibrations, frequency, amplitude, 3DEC, numerical
modeling
Abhinav Sharma
Student’s Signature
December 4th, 2017
Date
ESTIMATING THE EFFECTS OF BLASTING VIBRATIONS ON THE
HIGH-WALL STABILITY
By
Abhinav Sharma
Dr. Jhon Silva-Castro
Director of Thesis
Dr. Zacharias Agioutantis
Director of Graduate Studies
December 4th, 2017
(Date)
DEDICATION
This thesis is dedicated to my mother, father, and family.
I have been extremely fortunate to have been brought up by them, who
instilled in me the desire to continue my education. Without their help and
support, this research would not have been possible.
iii
ACKNOWLEDGEMENTS
I would like to express my deepest gratitude to all those who provided insight and expertise
that greatly assisted this research.
I am thankful to Dr. Jhon Silva-Castro who gave me the opportunity to join his research
team. I am extremely grateful to Dr. Silva who has been a great advisor and mentor. His
guidance helped me at all the stages of the project and writing of this thesis. He consistently
allowed this research to be my own work but steered me in the right direction whenever I
needed it.
I would like to thank Dr. Kyle Perry who accepted my application to join the Department
of Mining Engineering at the University of Kentucky. I would like to thank Dr. Perry and
Dr. Michael Kalinski for being part of my Thesis Committee and giving the valuable
inputs.
I am thankful to The National Institute for Occupational Safety and Health (NIOSH) for
having funded the research. I would like to extend my sincere thanks to the Nally & Gibson
management, for facilitating us to conduct the field study at their Georgetown Limestone
Quarry and for all their efforts in ensuring successful data collection.
I would like to express my sincere gratitude to my fellow graduate students especially
without whom conducting the various test programs and field data collection for this
project would have been impossible. Further thanks to the whole Mining engineering
department for creating a wonderful atmosphere, which made my stay at the department
truly memorable.
Finally, I would like to thank my family for all their support and encouragement.
iv
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ............................................................................................... iii
TABLE OF CONTENTS ................................................................................................... iv
LIST OF TABLES ............................................................................................................. vi
LIST OF FIGURES .......................................................................................................... vii
1 Introduction ................................................................................................................. 1
1.1 Background ............................................................................................................... 1
1.2 Blasting Vibrations .................................................................................................... 2
1.1 Problem Statement .................................................................................................... 4
1.2 Supplemental Tools ................................................................................................... 5
1.3 Organization of the Thesis ........................................................................................ 6
2 Literature Review ........................................................................................................ 7
2.1 Blasting Vibrations .................................................................................................... 7
2.1.1 General Characteristics of Blast Vibrations ........................................................... 8
2.1.2 Movement of the waves ......................................................................................... 9
2.1.3 Parameters describing vibration ........................................................................... 12
2.1.4 Vibration Amplitude ............................................................................................ 13
2.1.4 Vibration Frequency ............................................................................................. 15
2.2 Slope Stability ......................................................................................................... 17
2.2.1 General modes of Slope failure ............................................................................ 20
2.2.2 Mechanical approach to Stability Analysis .......................................................... 22
2.3 Attempts at studying and preventing effects of vibration on Slope Stability .......... 24
2.3 Numerical Modeling ............................................................................................... 33
2.3.1 Numerical Modeling application in Slope Stability Analysis .............................. 36
2.4 Vibration Standards ................................................................................................. 37
3 Experiment................................................................................................................. 42
3.1 Experiment Stages ................................................................................................... 42
3.1.1 Field data collection ............................................................................................. 43
3.1.1.1 Seismograph Setup ............................................................................................ 44
3.1.1.2 Site Scanning ..................................................................................................... 44
3.1.2 Data Processing .................................................................................................... 45
3.1.2.1 Scanner Data Processing ................................................................................... 46
v
3.1.2.2 Vibration Data assessment ................................................................................ 46
3.1.3 Numerical Modeling ............................................................................................ 47
3.2 Calibration of the Model ......................................................................................... 49
3.3 Parametric Study ..................................................................................................... 50
3.3.1 Establishing the natural frequency of the 100ft model ........................................ 53
3.3.2 Effect of height of the high-wall on natural frequency ........................................ 60
3.3.3 Effect of slope of the high-wall on natural frequency .......................................... 61
3.3.4 Effect of the amplitude of the vibration on natural frequency of high-wall ........ 65
4 Results ....................................................................................................................... 67
5 Conclusions and Recommendations .......................................................................... 70
5.1 Future Course of Action .......................................................................................... 71
Appendix ........................................................................................................................... 72
A. Variation in the natural frequency with the height of high-wall .................................. 72
A1. Model: 300ft and 90 degrees .................................................................................. 72
A2. Model: 500ft and 90 degrees .................................................................................. 75
B. Variation in the natural frequency with the slope of high-wall .................................... 78
B1. Model: 100ft and 65 degrees .................................................................................. 78
B2. Model: 100ft and 30 degrees .................................................................................. 82
C. Variation in high-wall natural frequency with the amplitude of vibration .................. 85
C1. Model: 100ft and 3 in/s Amplitude ......................................................................... 85
C2. Model: 100ft and 5 in/s Amplitude ......................................................................... 88
Bibliography ..................................................................................................................... 91
VITA ................................................................................................................................. 95
vi
LIST OF TABLES
Table 1-1: High-wall fatalities compared with total surface mining fatalities (MSHA,
2017) ............................................................................................................................ 2
Table 2-1: Range of typical blast parameters ................................................................... 13
Table 2-2: DGMS prescribed permissible limits for ground vibration in India ............... 41
Table 3-1: Properties of Limestone assigned in model ..................................................... 47
Table 3-2: Various parameters considered for the study and their variations .................. 51
Table 3-3: Variation in Natural Frequency with Height of the High-wall ....................... 61
Table 3-4: Variation of the Natural Frequency of the high-wall with Slope angle .......... 65
Table 3-5: Effect of change in amplitude on Natural Frequency of High-wall ................ 66
vii
LIST OF FIGURES
Figure 1-1: Typical high-wall mining operation (contourmining.com, Sep 20, 2017) ....... 1
Figure 1-2: USBM RI 8507 Safe Blasting Levels .............................................................. 3
Figure 1-3: High-wall under study at Nally & Gibson, Limestone Quarry, Georgetown,
Kentucky...................................................................................................................... 5
Figure 2-1: A typical seismograph (Source: Glossary, Blasting Training International) ... 8
Figure 2-2: A seismograph record measured in the field with all the three dimensions .... 9
Figure 2-3: Movement of the body waves from the blast-hole (M.S. Far et. al, 2016) .... 10
Figure 2-4: A general distinction of the three wave types monitored at large distance from
blast-hole (Geological Digressions, Archives Geophysics) ...................................... 11
Figure 2-5: Particle motion variation with wave type (Weebly, Earthquakes) ................. 12
Figure 2-6: Sine wave with repetitive motion with time (Introduction to Waves,
Wordpress) ................................................................................................................ 14
Figure 2-7: FFT of a signal giving a frequency distribution curve ................................... 16
Figure 2-8: Slope Configuration (Arteaga et. al, 2014) .................................................... 18
Figure 2-9: Orientation of a plane (Engineering 360, Geotechnical Services Information)
................................................................................................................................... 19
Figure 2-10: Different modes of slope failure in rock masses (R.Rai, Slope Lecture) ..... 21
Figure 2-11: Block on an inclined plane at limiting equilibrium (Rock Slope Stability,
C.A. Kliche)............................................................................................................... 23
Figure 2-12: Pre-split formation through instantaneous initiation of closely spaced holes
(P.Dunn, 1995) .......................................................................................................... 26
Figure 2-13: Approximate Powder Factor in Cushion Blasting (C.J. Konya, 1980) ........ 28
Figure 2-14: Section-view of Non-Pre-Split Final Design ............................................... 29
Figure 2-15: Design for the third trial ............................................................................... 30
Figure 2-16: East Ramp High-Wall of the mine ............................................................... 32
Figure 2-17: Single hole blast vibration Power Spectrum ................................................ 32
Figure 2-18: Transient vibration guide values for the cosmetic damage BS 5228-2:2009
................................................................................................................................... 38
viii
Figure 2-19: DIN-4150 (3) Vibration velocity levels for the evaluation of the short term
and long-term impact ................................................................................................. 39
Figure 2-20: Building categories, SN 640312 .................................................................. 40
Figure 2-21: Frequency range for the various building types ........................................... 40
Figure 3-1: Experimental setup process of the research ................................................... 42
Figure 3-2: High-wall under study at Nally & Gibson, Limestone Quarry, Georgetown,
Kentucky.................................................................................................................... 43
Figure 3-3: Setting up seismograph in field for data collection ........................................ 44
Figure 3-4: Maptek I-Site 8800 Scanner used to scan high-wall in field ......................... 45
Figure 3-5: Model generated by I-Site software from scan data collected in field ........... 46
Figure 3-6: Vibration data accessed using Seismograph Data Analysis ........................... 47
Figure 3-7: 3D model with boundary conditions for the numerical model in 3DEC ....... 48
Figure 3-8: Schematic 2D diagram of a 100ft model for the analysis .............................. 49
Figure 3-9: Velocity record data collected in the field ..................................................... 50
Figure 3-10: Calibration of the model by using the field vibration data .......................... 50
Figure 3-11: An artificial ground vibration sine wave with a frequency of 5 Hz ............. 52
Figure 3-12: Output Displacement at the crest on various Input Shear Wave Frequencies
................................................................................................................................... 53
Figure 3-13: The X-displacement time history for the 5 Hz stress wave on 100ft model 54
Figure 3-14: The X-displacement contour for the 5 Hz stress wave on 100ft model ....... 54
Figure 3-15: The X-displacement time history for the 20 Hz stress wave on 100ft model
................................................................................................................................... 55
Figure 3-16: The X-displacement contour for the 20 Hz stress wave on 100ft model ..... 55
Figure 3-17: The X-displacement time history for the 30 Hz stress wave on 100ft model
................................................................................................................................... 56
Figure 3-18: The X-displacement contour for the 30 Hz stress wave on 100ft model ..... 56
Figure 3-19: The X-displacement time history for the 30 Hz stress wave on 100ft model
................................................................................................................................... 57
Figure 3-20: The X-displacement contour for the 38 Hz stress wave on 100ft model ..... 57
Figure 3-21: The X-displacement time history for the 50 Hz stress wave on 100ft model
................................................................................................................................... 58
ix
Figure 3-22: The X-displacement contour for the 50 Hz stress wave on 100ft model ..... 58
Figure 3-23: The X-displacement time history for the 60 Hz stress wave on 100ft model
................................................................................................................................... 59
Figure 3-24: The X-displacement contour for the 60 Hz stress wave on 100ft model ..... 59
Figure 3-25: Displacement vs Frequency, with 38 Hz natural frequency of the 100ft high-
wall ............................................................................................................................ 60
Figure 3-26: The X-displacement time history for the 20 Hz stress wave on 100ft model
................................................................................................................................... 61
Figure 3-27: The X-displacement contour for the 20 Hz stress wave on 100ft model ..... 62
Figure 3-28: The X-displacement time history for the 28 Hz stress wave on 100ft model
................................................................................................................................... 62
Figure 3-29: The X-displacement contour for the 28 Hz stress wave on 100ft model ..... 63
Figure 3-30: The X-displacement time history for the 44 Hz stress wave on 100ft model
................................................................................................................................... 63
Figure 3-31: The X-displacement contour for the 44 Hz stress wave on 100ft model ..... 64
Figure 3-32: The X-displacement time history for the 55 Hz stress wave on 100ft model
................................................................................................................................... 64
Figure 3-33: The X-displacement contour for the 55 Hz stress wave on 100ft model ..... 65
Figure 4-1: Line Graph between Natural Frequency and High-Wall Height ................... 67
Figure 4-2: Variation of Natural Frequency with Slope of High-Wall for various heights
................................................................................................................................... 68
Figure 4-3: Comparison of Displacement and Frequency with Amplitude of 1 in/s & 3
in/s ............................................................................................................................. 69
1
1 Introduction
1.1 Background
Usually, after an open-pit mine excavation, a high-wall remains which is either abandoned
or covered. But with the development of high-wall miners, they are sometimes left to
recover the precious mineral in the future to justify the ever-increasing high stripping cost
in open-pit mining or in some cases support the underground excavation. These two facts
have resulted in larger high-walls that are left standing for increased periods of time prior
to reclamation. These long-standing high-walls with constant exposure to wear and tear of
mining operations, natural processes like rain, snow etc. have resulted in greater exposure
to the risk for miners and an elevated probability of serious accidents, which have
sometimes turned out to be fatal. Figure 1-1 shows a typical high-wall mining operation in
the Appalachian region in the USA.
Figure 1-1: Typical high-wall mining operation (contourmining.com, Sep 20, 2017)
2
The total number of surface mining fatalities has always been a concern and remains the
top priority for the mines. The modernization, improved studies, increased focus on safety
has helped in reducing the numbers as compared to past, but it is still high from the coveted
target of zero fatalities. Since 2005, the fatalities related to high-wall failures are close to
9.5% (Table 1-1) of the total fatalities in surface mining. Most of the modern surface
mining fatalities are associated with machinery and haulage.
Table 1-1: High-wall fatalities compared with total surface mining fatalities (MSHA, 2017)
Year High-wall
Failure
Fatalities
Total
Surface
Fatalities
Year High-wall
Failure
Fatalities
Total
Surface
Fatalities
2017 1 10 2010 0 3
2016 1 10 2009 0 4
2015 0 12 2008 1 5
2014 0 14 2007 2 7
2013 1 10 2006 1 6
2012 0 3 2005 0 2
2011 2 8 Total 9 94
The high-wall stability is a problem that is affected by various factors like, geology,
discontinuities in the rock mass, stresses, mining operations, standing time, weathering due
to surroundings and many others. But of them all, one of the important factors that is
relatively less talked or emphasized upon is the blasting induced stress, which over the
period can result in devastating outcomes when least expected.
The current study aims to delve into the forefront of understanding the effects of these blast
-induced stresses on a high-wall and determine the extent to which and how these stresses
affect the stability of high-wall.
1.2 Blasting Vibrations
Blasting of rocks using explosives remains the cheapest, simplest and most widely used
method to fragment and heave rock for the construction and mining industries. Part of the
energy released in the process of blasting is used for fragmenting or moving the rock, and
a part of the energy released during the chemical process is wasted in the form of heat,
vibration, sound, etc. Out of these various parts of energy that are not utilized for the rock
fragmentation and movement, vibrations and sounds are the most studied and observed
3
parameters. Sounds and vibrations effects of a mining blast are more perceptible to humans
and can have significant damaging effects on both humans and structures.
Based, on the damaging effects and human perception studies, various leading government
organizations across the countries established maximum recommended levels of vibrations
and sound generated from mining and construction operations to operate and to safeguard
structures. One of such organizations was the United States Bureau of Mines (USBM).
After years of research, a Report of Investigation (RI) 8507 was released by USBM, which
the main contribution to the mining industry is shown in Figure 1-2 and is known as the Z
curve.
Figure 1-2: USBM RI 8507 Safe Blasting Levels
According to the Z curve, any ground vibration (the peak particle velocity or PPV)
produced by a mining operation above the solid line will generate damage to the structures.
If the PPV is below the line, the safety of the structure without damage is assured. Another
important concept as per the Z curve is that the mining operations can operate at higher
PPV values if the generated blast vibration is composed of a high-frequency content. So,
4
usually, it is a general practice in mining to “shift” the ground vibration frequencies
produced by blasting to higher levels to prevent damage to structures. However, as
mentioned before, the Z curve was developed for the safety of structures (one story rural
houses) under certain blasting conditions and cannot be applied to high-walls. The levels
of vibrations and frequencies which affect high-walls could be different from mine to mine,
and damaging effects might not govern from the usual blasting standards set for human
structures.
1.1 Problem Statement
The current research investigates the impacts of the dynamic stresses generated due to
blasting on the high-walls and tries to correlate its damage to blasting vibration,
frequencies, amplitude, and duration.
The research is divided into two phases, where in Phase 1, the focus is the on collection of
the field data by setting up seismographs to record blasting vibrations and use of a scanner
to collect the scan data of walls. Phase 2, of the research, is the parametric study based on
the calibrated numerical model to understand the relationship between parameters like
frequency, geometry on the stability of high-walls.
Phase 1
The first part of the research concentrates on studying high-wall as shown in Figure 1-3
and the case under study is Nally and Gibson, Georgetown Limestone Quarry located in
Georgetown Kentucky, where the underground excavation of limestone is done using drill
and blast.
Phase 1 was carried out in two stages with field data collection of vibration histories and
scan data of the high-walls at various stages. The vibration histories collected from the
field were used as an input to calibrate the model in Phase 2 of the project. The scanned
data collected using the Maptek I-Site 8800, is used to design surfaces and could be used
as an input for the Three-Dimensional Discrete Element Code (3-DEC) for further
numerical simulation. In the present research, due to time constraint, this was not utilized,
but it can be a further course of the study for the future work.
5
Figure 1-3: High-wall under study at Nally & Gibson, Limestone Quarry, Georgetown,
Kentucky
Phase 2
Usually, the mines look for the established government regulations for guidance to
determine the peak particle velocity and frequency levels. But most of the regulations
around the globe are meant for the structures surrounding mine and does not concern high-
walls.
The parametric study in this phase explores numerical models in 3DEC to understand the
impact of parameters like the geometry of the slope, the frequency, the amplitude, and the
duration of the blasting vibrations on high-wall stability. The models in use were calibrated
initially with data collected from seismographs in the first phase of the research. The study
also tries to explore if the any of the outcomes can help the mines to design their blast more
prudently.
1.2 Supplemental Tools
Various tools were the key to achieving the outcome of the research. They were important
in various stages of the research.
6
In the primary stage of the field data collection, following tools made the basis for it:
1. Seismographs
The seismograph was set up to collect the vibration, frequency, amplitude of the blast
vibrations. The data collected by the seismographs is accessed remotely using a modem
used to transmit data.
2. Maptek-I-Site Laser Scanner
The high-wall under study was scanned using Maptek I-Site 8800. The scanner is set up in
the field at multiple locations, usually three, to cover the high-wall from all the angles. The
scanner takes a 360° picture of the area and the picture is divided into multiple sections to
scan as per the requirement. The scanned data is stored in a portable hand-held controller
which can be later imported to a personal computer for further processing.
3. Three-Dimensional Discrete Element Code (3DEC)
3DEC is a three-dimensional numerical program based on the distinct element method for
discontinuum modeling from Itasca. This numerical program allows finite displacements
and rotations of discrete bodies, including complete detachment (User’s Guide 3DEC
version 5.0). It has a command driven structure for programming. The various numerical
models for the parametric study were generated using the 3DEC.
1.3 Organization of the Thesis
The thesis is divided into five main chapters. Chapter 1 provides the background leading
to the research. It also discusses the purpose of the project. Chapter 2 is focused on the
literature review and discusses the previous attempts to study the high-wall stability.
Chapter 3 focuses on the experiments and the setup for the research. Chapter 4 discusses
the outcomes of the results of the study. Finally, chapter 5 summarizes the results and
conclusions.
7
2 Literature Review
2.1 Blasting Vibrations
Vibrations can be described as a passage of the energy which oscillates the particles of the
material about an average position. The vibrations at a point could be of the low intensity
or the high intensity depending on the various parameters like the source of energy,
distance from the source, mode of transportation of energy etc.
Ground vibrations due to blasting are a similar passage of the energy, released from the
blasting operations in mines, quarries, and other construction activities. Vibrations need a
medium to travel, which is different from light and electromagnetic waves that can travel
within the vacuum. As the name suggests, ground vibrations propagate through the earth
and are sometimes termed as seismic waves as their propagation properties are similar to
the ground motions produced by earthquakes (David Siskind, 2005). But blasting
vibrations are primarily different with their low peak amplitude and high dominant
frequencies than earthquakes due to the source of energy and lower distance of
propagation.
To understand these ground vibrations, they are measured in terms of velocity,
displacement or acceleration at the point of interest. The seismograph as shown in Figure
2-1 is an instrument that records vibrations of the particle in all the three directions i.e.
vertical, transverse and longitudinal to understand the complete movement. The time
history recorded by these seismographs is a waveform, a continuous representation of the
particle movement.
8
Figure 2-1: A typical seismograph (Source: Glossary, Blasting Training International)
2.1.1 General Characteristics of Blast Vibrations
The passage of the ground vibrations makes the ground to move in an elliptical manner in
three dimensions. To understand and measure this movement the motion is recorded in all
the three dimensions, longitudinal, transverse and vertical as shown in the Figure 2-2. In
the given figure, the X-axis is time and Y-axis is the velocity measured continuously at all
point of times on the curve. Longitudinal component is usually along the horizontal
direction of explosion and other two components are perpendicular to it with, vertical being
vertical and transverse being in the radial direction.
The three wave types are divided into two varieties:
1. Body Waves
2. Surface Waves
Body waves are the waves that travel through the body of the rock and soil, whereas surface
waves propagate along a surface-air interface.
9
Figure 2-2: A seismograph record measured in the field with all the three dimensions
Body waves are further divided into two types:
1. Primary waves (P-wave)
2. Shear waves (S-wave)
Primary waves are compressive in nature and the shear waves are distortional in nature.
The surface waves are more commonly known as Rayleigh waves and become significant
usually at a distance from the source of the blast.
2.1.2 Movement of the waves
A blast hole explosion results in the generation of the body waves at small distances. These
waves propagate in a spherical manner as shown in the Figure 2-3, are pre-dominantly the
P-waves, which on intersection with a crack or fracture or any other rock type results into
the generation of the shear and surface waves.
10
Figure 2-3: Movement of the body waves from the blast-hole (M.S. Far et. al, 2016)
At small distances, usually, all the three wave types reach at the same time and it is difficult
to identify them. But at large distances, the shear wave and the surface waves which are
relatively slow as compared to the compressive waves are easy to distinguish as shown in
Figure 2-4.
In blasting operations, the blast-holes fire in a sequence of few milliseconds resulting in
overlapping of the waves and makes it a difficult phenomenon to understand. But single
hole shots study (Reihart, 1975) gave a better understanding of the effects of the blasting
vibrations.
Usually, the blasting personnel are not concerned about the individual types of the waves
and focus on measuring and analyzing the highest amplitude for the purpose of blast design.
But sometimes the wave type is also of concern when the generation mechanism is relevant.
11
Figure 2-4: A general distinction of the three wave types monitored at large distance from
blast-hole (Geological Digressions, Archives Geophysics)
The three waves create a completely different movement of the particle when they pass
through rock or soil as shown in the Figure 2-5. Thus, they have the different effect on the
structure concerned. The longitudinal wave (P-wave) generates motion of the particle in
the direction of propagation, the shear wave (S-wave) produces motion perpendicular to
the direction of propagation. The surface wave (Rayleigh wave) generates motion of the
particle both in the perpendicular and parallel direction of propagation.
12
Figure 2-5: Particle motion variation with wave type (Weebly, Earthquakes)
2.1.3 Parameters describing vibration
A typical particle motion time history graph i.e. a vibration plot is described mainly by the
following:
1. Peak amplitude
2. Principal frequency
3. Duration of the motion
These parameters are dependent on various properties such as the strength of the rock,
propagation medium, and the blasting sequence or blast timing. The range of parameters
determining the characteristics of the vibration for general mine blasting, quarrying, and
construction operations are presented in the Table 2-1 (Cording et al. 1975).
13
Table 2-1: Range of typical blast parameters
Parameter Range
Displacement 10-4 to 10 mm
Particle Velocity 10-4 t 103 mm/s
Particle Acceleration 10 to 105 mm/s2
Pulse Duration 0.5 to 2 s
Wavelength 30 to 1500 m
Frequency 0.5 to 200 Hz
The two important characteristics that make a blast vibration different from the earthquake
are:
1. The vibrations occur at relatively higher frequencies as compared to earthquake
2. The energy contained in the motion is minute as compared to an earthquake
2.1.4 Vibration Amplitude
The particle motion is most commonly measured in the form of displacement, velocity or
acceleration. Most of the current seismographs measure velocity and the major safety
regulations set up by the countries also have velocity limits.
To study blasting vibrations they are approximated as sine waves varying in time or
distance. The approximation helps in simple conversions in between the velocity,
acceleration, and displacement.
The general form of sine wave used in blasting vibrations can be understood with equation
for the displacement, u,
u = U sin (Kx + ωt) (2.1)
where;
U is maximum displacement
K is constant know as wave number
ω is circular natural frequency
14
t is time
If the location and wavelength are constant, the variation of displacement with time can be
written as;
u = U sin (constant+ ωt) (2.2)
As can be seen from the Figure 2-6, the wave repeats itself after a certain fixed time called
as the period T, ω must be equal to 2π/T to make the function repeat when time moves by
a period. As frequency is the number of times waves repeats itself in a second, so frequency
is equal to 1/T. So, the circular natural frequency can be given as,
ω =2π/T (2.3)
f =1/T (2.4)
ω = 2πf (2.5)
Figure 2-6: Sine wave with repetitive motion with time (Introduction to Waves, Wordpress)
The wavelength similarly, can be given in terms of the propagation velocity c and period
T, as
u = U sin (constant + ωt) (2.6)
v = U ω cos (constant+ ωt) (2.7)
a = -U ω2 sin (constant + ωt) (2.8)
15
So, the absolute value of the maximum motion can be given by the following when sine
function is equal to 1.
λ = c/f (2.9)
u = U
(2.10)
v = 2πf U (2.11)
a = 4π2f2U (2.12)
Thus, the maximum particle motion can be found easily from one another, in sine wave
approximation of the wavelength, if frequency f is known.
In general, when all the three components of the particle motion are observed, i.e. the
longitudinal, transverse and the vertical, none of them always dominates and peak
component is different in different blasting situations. The peak value does not occur at the
same time for the different components. So, for the sake of clear understanding, the peak
particle motion is described as the magnitude of the highest particle motion of any of the
three components. Another value, maximum vector sum is calculated by taking the square
root of the summation of the squares of the maximum of each component, making it by
default a larger value than any of the individual maximum value of any of the component.
Thus, this value gives a safety factor giving a guidance as most of the observed empirical
cracking is done by single-component peaks.
2.1.4 Vibration Frequency
The frequency of a wave as discussed before is the number of times a wave repeats itself
in a second. Previous research has shown that structures respond differently when excited
by vibrations, equal in all respects, but differing in principal frequency (Charles Dowding,
2000).
Vibration frequency can be calculated in a variety of ways like Fast Fourier Transformation
(FFT), inversion of time periods and response spectrum techniques. The FFT as shown in
Figure 2-7 is useful in understanding and processing a signal (vibration time history),
which is converted into a frequency distribution to determine the dominant frequency.
16
Response spectrum also displays frequency distribution, and frequency and period work
with function f=1/T.
Figure 2-7: FFT of a signal giving a frequency distribution curve
The single-degrees-of-freedom (SDF) systems are the base of the frequency and the
distance related blasting guides (Siskind et al. 1980b). In the well-known mug-rubber
experiment, which behaves like an SDF system, it was established that the frequencies
higher than the natural frequency cause less strain or displacement. This, later on, became
the base for, why it is important to determine the dominant frequency of vibrations for
controlling the potential to cause cracks.
Vibration frequency is sensitive to absolute distance and nature of the transmitting media.
The vibrations traveling through rock retain the higher frequencies in contrast to the soil as
a transmitting media. Soil layers over rock produce low-frequency vibrations through both
selective attenuation and the generation of surface waves.
Vibration frequencies are possibly related to the initiation sequence intervals; however, this
effect is usually masked by the scatter in the timing, but nowadays the improved initiation
17
systems can relate better to predicting the vibrations. RI 8507 (Siskind et al. 1980b)
describes the importance of various design parameters and studies done to identify their
relative importance.
2.2 Slope Stability
A slope can be defined as an inclined surface cut into the natural body, which is usually
expressed as the degrees of inclination with respect to the horizontal. Slope designing in a
mine is a very crucial engineering task. It is vital for the mine to have a well-planned and
designed slope both from the safety and economic point of view. Slope designing in a mine
is a task which is governed by the proper integration of three important divisions: Planning,
Production, and Geo-mechanics.
Slope Configuration
The basic terms associated with the slope configuration are shown in Figure 2-8. The some
of the important terms to be known are:
1. Crest: The top of an excavated bench
2. Face: The inclined or vertical surface of the rock exposed after excavation
3. Bench: A base that works as a single level of operations in an open-pit mining
4. Bench Angle: The angle of the bench w.r.t the horizontal
5. Toe: The bottom of the slope
6. Overall Slope Angle: The angle formed by a line joining the toe of the wall to the crest
of the wall with respect to the horizontal.
18
Figure 2-8: Slope Configuration (Arteaga et. al, 2014)
Slope Orientation
Orientation of a slope is defined by the following terms which are shown in the Figure 2-9
1. Dip: The angle at which a bed is inclined from the horizontal, measured normal to strike
and in the vertical plane
2. Dip direction: the direction perpendicular to the strike, which is bearing of the dip
3. Strike: The outcrop of a fault plane or bed on a level surface
19
Figure 2-9: Orientation of a plane (Engineering 360, Geotechnical Services Information)
Slope Failure: Causes and Processes
Stability of a slope is dependent on several factors and it is difficult to point out any single
cause for the failure of the slope. In general, it is a combination of certain factors combined
at a time to cause the failure. These factors are divided into two categories:
1. Factors causing increase in Shear Stress
2. Factors reducing the Shear Strength
Increased Shear Stress
The major factors which fall into this category are:
1. The increased amount of load on a slope like that in a case of dumping excess material
in an internal mine dump slope
2. Transient dynamic stresses from the blasting operations, movement of heavy mining
equipment and earthquakes
20
3. Lateral pressure due to pore pressure, widening of cracks due to inclement weather
conditions
4. Increased tectonic activities that can disrupt the stress fields
Reduced Shear Strength
The major factors which fall into this category are:
1. Inherent characteristics of the material or the geological factors such as orientation and
presence of the discontinuities, the presence of the weak material.
2. The removal of the sideways support, in the case of mines it could be due to removal of
the retaining structures, the soil erosion due to rainy conditions or the subsidence
3. Changes in the strength due to weathering, like the physical breakdown of the granular
rocks resulting in reduced cohesion.
4. Changes in the internal forces due to discontinuities and water pore pressure
5. Weakening of the slope due to continuous creep.
2.2.1 General modes of Slope failure
The four primary modes of slope failure are:
1. Plane Failure
2. Circular Failure
3. Wedge Failure
4. Toppling Failure
The other modes of failure that are considered as slope failure include rockfalls and rock
flow. All the four primary modes of failure are shown in the Figure 2-10
21
Figure 2-10: Different modes of slope failure in rock masses (R.Rai, Slope Lecture)
1. Plane Failure
Planar failure can occur where weak planes such as joints, faults, and bedding planes dip
into the excavation due to unfavorable face orientation. A build-up of high water pressures
may lead to sudden failure where critical planes daylight in the quarry face. Tension cracks
can also be monitored for movement.
2. Circular Failure
These can occur in high faces in weak materials such as silts and clays, heavily jointed
rock, tailings and spoil heaps. Loading at the crest of the slope and toe excavation
combined with high water pressures may lead to failure. Tension cracks may form behind
the slope and these can be monitored to give some indication of the progress of the
movement.
3. Wedge Failure
22
Wedge sliding in mutually inclined and intersecting planes can occur where weak planes
dip into the excavation due to unfavorable face orientation. The buildup of high water
pressures may lead to sudden failure where critical planes daylight in the quarry face.
4. Toppling Failure
This occurs in hard rock with columnar structure and over-steep faces with closely spaced
and adversely inclined steep discontinuities dipping into the face. The resulting movement
is due to forces that cause an over-turning moment about a pivot point below the center of
gravity of the block. If unchecked, it will result in a fall or slide of the material.
2.2.2 Mechanical approach to Stability Analysis
The stability analysis of the slope has been approached in numerous ways, including
probabilistic methods, static equilibrium methods, finite difference or element methods and
many more. The most common method employed is the simple limit equilibrium method
to evaluate the sensitivity of possible failure conditions to slope geometry and rock mass
parameters (Piteau and Martin, 1982). The other detailed methods such as finite element
or probabilistic analysis are taken into consideration when the stability of the slope is
sensitive to the failure mechanisms. Limit equilibrium technique is usually applied in the
cases where the failure mechanism and the strength parameters can easily be defined, for
the more complex issues where a large amount of discontinuities, complex geometry is
involved, advanced techniques are considered.
The Limit Equilibrium Concept
The limit equilibrium concept, as the name suggests is the point in time when the driving
forces are just equal to the resisting forces, which in turn means that all the points are on
the verge of failure. This gives rise to the fact that, the factor of safety will be greater than
unity, the i.e. slope will be considered stable, when the resisting forces are greater than the
driving forces and less than unity otherwise, meaning an unstable slope.
The simplest approach to a limit equilibrium concept can be observed in the case of planar
failure, where a block rests on the inclined slope as shown in the Figure 2-11.
23
Figure 2-11: Block on an inclined plane at limiting equilibrium (Rock Slope Stability, C.A.
Kliche)
The following equations describe the forces acting on the block
𝜏 = 𝐶 + 𝜎𝑡𝑎𝑛𝜑 (2.13)
𝜎 =
𝑁
𝐴= 𝑊𝑐𝑜𝑠𝛽/𝐴
(2.14)
𝜏 = 𝐶 + (
𝑊𝑐𝑜𝑠𝛽
𝐴) 𝑡𝑎𝑛𝜑
(2.15)
Shear force = 𝜏𝐴 = resisting force = 𝐶𝐴 + 𝑊𝑐𝑜𝑠𝛽 ∗ 𝑡𝑎𝑛𝜑 (2.16)
Driving force = 𝑊𝑠𝑖𝑛𝛽
(2.17)
Equating driving and resisting forces we get equation for factor of safety (F.S.)
F.S. = Resisting Forces/Driving Forces = (𝐶𝐴 + 𝑊𝑐𝑜𝑠𝛽𝑡𝑎𝑛𝜑)/ 𝑊𝑠𝑖𝑛𝛽 (2.18)
24
here,
𝜏 = shear stress along the failure plane
𝐶 = cohesion along the failure plane
𝜎 = normal stress on the failure plane
𝜑 = angle of internal friction for the failure plane
𝑁 = magnitude of the normal force across the failure plane
𝐴 = area of the base of the plane
𝑊 = weight of the failure mass
𝛽 = dip angle of the failure plane
2.3 Attempts at studying and preventing effects of vibration on Slope Stability
As detailed in the previous sections, transient vibrations from the mine blasting and
earthquakes are one of the driving factors in slope failures. As discussed earlier, the two
important parameters when understanding vibrations are its amplitude and frequency. So,
to mitigate the effects of vibrations on slope stability it has been long studied by various
researchers, mines how they can control these two parameters of the vibration so that they
do not affect the slope or high-wall in their mine or the subject of the study. The guidelines
for controlling these parameters are introduced by the government organizations and
authorities in the respective country of the study.
The common methods used by the mines or the researchers for reducing the effects of
these parameters are:
1. Contour Blasting
2. Frequency Shifting
Contour Blasting:
The energy that is not used for fragmentation or displacement of the rock, sometimes 70-
80% of that developed in a blast hole, is mostly responsible for the strength reduction of
the rock outside the radius of excavation. New fractures and planes of weakness are created
and joints and bedding planes that may have been stable before the blast but can be opened.
As a result, the rock mass stability can be reduced. This can be seen as over break and the
25
fractured face is left with a higher likelihood of rock falls. Thus, to address such technical
and economical adversities it is required to put up an appropriate level of engineering effort
that can produce safe and stable high-wall. This engineering effort is termed in the mining
industry as “Contour/Perimeter Blasting”.
Types of Contour Blasting
There are various types contour blasting methods, of these the most commonly used are:
1. Buffer blasting
2. Pre-splitting
3. Cushion blasting
4. Line drilling
Buffer Blasting
This is one of the simplest ways of contour blasting. Usually, the last row of production
blasting is altered for the energy, by changing the blasting pattern. The explosive energy
in the row is decreased so does the spacing and burden. The explosive energy is reduced
by using a scaled depth of burial higher than usual or using a decoupled charge over the
base of fully coupled toe charge.
Buffer blasting could be used as the sole technique of the wall control when the rock is
competent. There might be some over break and fractures in the final wall, but would be
much less than the production shot. Usually, buffer blasting is used in conjunction with
other means of wall control, but when used alone it is very economical.
Pre-Splitting
Pre-split is a row of small diameter, blast holes with decoupled charges, which are usually
fired instantly before the production blast to create a fracture plane. Creation of a pre-split
fracture before the production shot considerably reduces the amount of tensile stresses
damaging the high-wall.
One of the important parameters in pre-split blasting is the use of lightly loaded holes. The
light powder load may be obtained by using specially designed slender cartridges, partial
26
or whole cartridges taped to a detonating cord downline, an explosive cut from a continuous
reel, or heavy grain detonating cord. A heavier charge of tamped cartridges is used in the
bottom few feet of the hole.
The depth for single pre-split is usually from limited to 45 to 60 feet due to the poor
accuracy of the drill holes of the small diameters. A deviation in the range of 5-6 inch from
the desired location can result in a poor pre-split outcome.
Usually, the pre-split holes are not stemmed, the decoupled charges and instantaneous
firing takes care of containing the gas pressure for the wedge effect. But if the noise from
the pre-splitting is a point of concern for the mining team, the holes could be stemmed but
could result in the crater formation at the crest.
Pre-split charges are fired using detonating cord, electronic detonators or the instantaneous
electric detonators as shown in Figure 2-12, to create the desired fracture plane. But,
wherever noise is a problem a small pyrotechnic delay detonator could be used to reduce
the maximum charge going off per delay. Surface lines of detonating cord should also be
buried with sand or the drill chippings to reduce the noise levels.
Figure 2-12: Pre-split formation through instantaneous initiation of closely spaced holes
(P.Dunn, 1995)
27
Cushion Blasting
Cushion blasting is a common practice in the surface mines to trim or remove the excess
material from the face to give a smooth wall with little over break. The blast holes for
cushion blasting are drilled along the final line of excavation, the coupled toe charge is
followed by a decoupled charge to reduce the damaging effect to final wall.
The common diameter for cushion blasting have varied from 4-7 inches but large holes are
also used in the big surface mines. For this range of hole diameters, the common spacing
used is in the range of 5-8 feet. The general thumb rule that could be useful is spacing in
feet is 1.25 to 2.0 times the hole diameter in inches, higher the values correspond to the
softer rock and lower to hard rock.
The trim row should be suitably decoupled, with the coupling ratio of 0.45 for clean and
smooth final wall. Decoupling could be achieved using the undersized cartridges or use a
suitable charge in the bottom of the hole and allow gases to move up the blast hole.
The timing consideration in case of cushion blasting is different from the pre-splitting, as
in here unlike pre-split, the trim row is blasted after the main blast. The trim row needs
sufficient relief to remove the excess material from the face, so it is necessary that enough
time gap is provided between the production and trim row blasting. Usually the trim row
detonates after one delay period after the adjacent production holes shot. Multiple trim
holes can be shot per delay provided they don’t fire before the production holes or they are
not exceeding the vibration limits defined for the site.
Cushion blasting usually has the similar blast hole diameter as that of the production shot.
The bigger diameter allows for the more accurate drilling as compared to pre-split blasting.
The accurate drilling, in turn, helps to create trim holes as deep as production shot which
is usually the one bench height.
Line Drilling
Line drilling is a method used seldom in surface mines as drilling closely spaced holes is
expensive. They are only used when the rock is very weak and highly fractured and it is
very difficult to do a pre-split or cushion blast.
28
The typical hole size for line drilling is from 2-3 inches. The costing is reduced if it possible
to use larger holes, as spacing could also be increased with it. But in most cases, the use of
small diameter blast holes due to fractured rock mass keeps the depth restricted to 30-40
feet.
Accurate drilling is the most important parameter in line drilling to be successful. The holes
drilled should all lie along the plane which corresponds to the final pit wall. Unequal
spacing can lead to variable results. Figure 2-13 displays initial values for the approximate
hole spacing in line drilling method. The hole spacing in feet could be determined by
multiplying the appropriate factor with drill diameter in use.
Figure 2-13: Approximate Powder Factor in Cushion Blasting (C.J. Konya, 1980)
In literature, we find various (C. Brown et. al, 1972, A. Rorke et.al, 2003, G. Newman et.al,
2011) examples of contour design blasts to reduce the damage to high-wall. One of the
cases discussed (K. Christopherson, 2011) in details is Morenci Mine, of Arizona, USA.
Case Study: Blast Designs in Morenci Mine
Overview
Morenci is an open-pit copper mine located in Greenlee County, Arizona. Ownership is
Freeport-McMoRan Copper & Gold, Inc. (85 percent) and Sumitomo Metal Mining
Arizona Inc. (15 percent). The open-pit has been in operation since 1937 producing over 7
billion tons containing over 31 billion pounds of salable copper.
Problem
The blast design for 10.625 in. holes, for the upper bench of a 100ft high-wall required a
trim row at half the typical production spacing drilled 2ft off the designed toe; the 2nd row
with typical production spacing drilled 18ft off the trim row; the 3rd row of the same
29
spacing drilled 18 ft. off the buffer row; and then standard production burden and spacing
into the pit. The design for the lower bench of a 100ft high wall required same dimensions
but moved 3ft in or 1ft inside of the design toe, in order to achieve the limit. This is
displayed in Figure 2-14
Figure 2-14: Section-view of Non-Pre-Split Final Design
It was established by the mining team that the blast achieved the designed toe but the final
charge weight resulted in the over break, damaging the high wall.
Results with new blast designs
Trial 1
To resolve the issue of the over break the charge weight in the trim row was reduced and
air deck was introduced in the first trial. The results were acceptable in terms of the over
break but the toe of the wall measure 20 ft.-30 ft. off the designed toe.
Trial 2
30
To resolve the issue of designed toe the trim row was brought closer to the mid-bench and
the second-row closer to the trim-row. The powder factor in buffer row was increased to
1.0 lb/yd^3. The design from the trial 1 was improved with stronger powder factor without
fear of damaging the high wall. The result from the blasts were better from the trial 1, but
still, the toe was off by 12 ft. to 20 ft. from the designed toe. It was concluded the buffer
row could not pull the toe as much is required with this powder factor.
Trial 3
To mitigate the issue, as shown in Figure 2-15 the trim row was placed in the mid-bench
and buffer row was maintained at the same spacing as in trial 2. The third trial achieved
both the objectives-a sound wall and achievable toe limit.
Figure 2-15: Design for the third trial
31
Frequency Shifting
Usually, mines or other blasting operations follow the statutory vibration standards for their
blasting operations. From the previous sections, we understand that the frequency is an
important parameter when defining displacement or strain at a given point or structure. For
example, for the same particle velocity at a single frequency vibration of 20 Hz, the
displacement will be half of the 10 Hz frequency vibration.
This concept of generating higher frequencies to stay at lower displacement levels is vital
for vibration sensitive areas. But before moving from one frequency to another it is vital to
understand the resonant or the natural frequency of the structure we want to protect. If in
the above case, if the natural frequency of the structure under study is 20 Hz, then it
coincides with the dominant frequency of the vibration, which can result in the excitation
of the structure giving rise to higher displacement or strain levels. So, it is important that
we find the natural frequency of the structure and then do the frequency shifting whether
it is to a lower or higher frequency. This approach has been researched and practiced in
many mines across the world, details of which could be found in the work of D.S.Preece
(2010), A. Sharma et.al (2013). One of the most recent approach by C. Dzerzhinsky (2016)
is discussed below.
Case: Shifting the blast vibration frequency to preserve high wall (Charles
Dzerzhinsky, 2016)
In this case, where the name of the mine was not disclosed in the paper, the high-wall in
the mine as shown in Figure 2-16, had troublesome geological conditions, which were
resulting in several failures. It was a concern for the Drill and Blast team of the mine that
by their actions of blasting near the wall they should not further aggravate this situation.
The most important parameter as we discussed above in shifting the frequency of vibration,
it is important to determine the ground resonant frequency. This is done mostly firing single
hole shots and collecting data using seismographs. As shown in the Figure 2-17, it was
found that the mine had the ground resonant frequency range between 9-12 Hz and the
ground was well able to support the frequencies in the range of 20-30 Hz.
32
Figure 2-16: East Ramp High-Wall of the mine
Figure 2-17: Single hole blast vibration Power Spectrum
33
So, it was feasible that with the correct study and use of blasting systems, the frequency
could be shifted away from the dominant frequency of the ground, in case the current
practices were generating vibration close to the ground dominant frequency.
Solution: The mining team did a range of study and concluded that the mine current
practices are generating vibrations levels close to the dominant frequency and they need to
shift away from it. The mine shifted to the blast timing regime of 40 ms between the holes
which resulted in the frequency shift in the range of 28-30 Hz well away from the resonant
frequency. It was observed by the geotechnical team of the mine after shifting to new
practices, over the period there was a decrease in the ground movement.
There are several other practical studies (Ruling Yang et. al, 2009) that have worked in the
direction of frequency shifting, which indicate that it is essential to first determine the
dominant frequency of the structure to preserve and then shift away from that frequency to
reduce the damage to the structure.
2.3 Numerical Modeling
The term "numerical modeling" is used for all types of calculations that are based on
numerical solutions of the complex differential equations encountered in rock mechanics
and engineering problems (R. Rai, 2012). Most of them apply discretization of the rock
mass into a large number of individual elements and achieve an iterative solution by
repetitive calculation in a computer. This technique is used mainly for the analysis of rock
stresses and deformations.
The basic pre-requisites for numerical analysis are the idealization of the actual excavation
within the rock mass and the division of the rock mass into different sectors, based on the
results of geological investigations. Material property models are established for each of
the sectors, and for the anticipated rock supports.
It is important to be aware of the restrictions and uncertainties that are inherent in such
modeling, of which the most important arise from the difficulty of obtaining reliable input
parameters, especially for:
- The magnitudes and directions of the in-situ stresses.
34
- The material model and properties of the in-situ rock mass.
- The location and extent of the various geological sectors within the rock mass.
The reliability of the analysis will never be better than the reliability of the input parameters
and applied models.
Numerical modeling is widely used to resolve complex slope stability problems. These
models are helpful in integrating and giving the required representation of the
discontinuities such as joints, faults etc.
The numerical methods used for the analysis are divided into three approaches:
1. Continuum modeling
2. Discontinuum modeling
3. Hybrid modeling
Continuum Modeling:
Continuum modeling is used mostly in for the slopes with massive and intact rocks. The
model assumes the material to be continuous throughout the body and discontinuities are
introduced as an interface. The model is not very suitable for the slopes with many
intersecting joints.
The finite difference, finite element, and the boundary element methods are based on the
continuum modeling approach. In this approach as a basic condition, the problem is broken
down into various elements by discretization and the solution is procedure is initiated based
on the numerical approximations of the equations.
There are both three dimensional and two-dimensional software based on the continuum
modeling, some of the examples are:
1. Fast Lagrangian Analysis of Continua (FLAC) 2D and FLAC 3D based on the finite
difference methods, used to model complex behaviors, unstable systems etc.
2. Phase 2 is a two-dimensional finite element method based software used for analysis of
the complex geotechnical issues.
35
3. PLAXIS 2D is also a two-dimensional finite element method based software widely used
for the slope stability analysis.
Discontinuum Modeling:
Discontinuum modeling methods consider rock mass under study as discontinuous by
treating them as a group of rigid or deformable blocks. These methods allow the slipping
and movement along the discontinuities with normal and shear stiffness, which allows
relative movement to one another and helps in modeling complex behavior. These methods
treat the problem as a group of distinct bodies interacting with one another and the external
loads. These are together termed as discrete element methods.
The variations of the discrete element methodology involve:
1. Distinct Element Method
2. Discontinuous deformation analysis
3. Particle Flow Codes
The most widely used discontinuum modeling based software used for the slope stability
analysis are UDEC (Universal Distinct Element Code, Itasca Consulting Group) and 3DEC
(3-Dimensional Distinct Element Code, Itasca Consulting Group).
Hybrid Modeling:
Hybrid modeling is an approach gaining popularity among the researchers as it can allow
the abilities of two different methods to be combined to achieve the desired results. GEO-
SLOPE could be as an example where the stress and water flow analysis is adopted using
limit equilibrium stability and finite-element method. Although, the requirement of high
memory for complex problems and little experience remains a challenge in the
development of this modeling.
Three-Dimensional Distinct Element Code (3DEC)
As discussed in the previous section 3DEC is based on distinct element method for
discontinuum modeling. 3DEC simulates the response of the media like jointed rock mass
subject to either static or dynamic loading.
36
The salient features of the 3DEC are (User’s Guide Itasca 3DEC, 5.0):
1. The rock mass is modeled as 3D assemblage of rigid or deformable blocks
2. Discontinuities are regarded as distinct boundary interactions between blocks
3. A joint structure can be built into the model from the geological mapping
4. 3DEC’s in-time solution algorithm can accommodate large displacement and rotation
5. The graphics facility permits interactive manipulation of 3D objects
3DEC was initially developed to study the jointed rock mass for slope stability. But it has
been used extensively in the mining engineering problems for both underground and open-
pit solutions in static and dynamic conditions. The blasting effects are studied using
dynamic stress or velocity waves at model boundaries. In our analysis, of the experiment,
we have used the stress wave analysis approach to solve the problem.
2.3.1 Numerical Modeling application in Slope Stability Analysis
Case Study: Slope Stability at Escondida Mine
The Escondida Mine is a copper mine discovered on March 14, 1981, in Antofagasta Chile
(Cristina Valdivia and Loren Lorig Slope Stability in Surface Mining, SME 2000).
Concern: The slope failure mechanism at the mine involved strong structural control with
the formation of non-daylighting wedges. The mine wanted to analyze the case of mining
the four benches without expanding the unstable area of the northeast corner of the mine.
Slope-Stability Analysis: The mine had been using the XSTABL a software based on the
two-dimensional limit equilibrium method and FLAC 2D for the analysis of the slope
stability. But they were not capable of analyzing the planar failure that allows rotation, slip
or separation of the deformation blocks.
Solution: The three major stability concerns of the mine were:
- A weak rock mass
- Strong structural control resulting in non-daylighting wedges
- High pore pressures
37
3DEC was employed by the mine which had the capability to consider all these factors.
After numerical analysis with 3DEC, mine operations could successfully excavate the four
benches without affecting the unstable area of the mine.
Other examples:
At the Barrick, Goldstrike mine, the numerical modeling (using UDEC) approach was used
to interpret the failure mechanism of the slopes and complement the more traditional design
assessments like limit equilibrium approach. (Nick D. Rose and Robert P. Sharon, SME
2000)
There are various other examples available where the numerical modeling has been used
as a preferred approach to resolving the slope stability problems.
2.4 Vibration Standards
Vibrations from the blasting, quarrying and construction activities have been a nuisance
and a hazard for a long time both for the humans and the surrounding structures. Over the
decades, countries and government authorities have become more and more vigilant and
rigorous in the application of the vibration standards.
In general, most of the countries developed the vibrations standards keeping the detrimental
effects of the blasting operations on the concerned man-made structures and human beings.
But still, most of these standards are utilized for the estimating the limits of construction
blasting, pile driving and for the structures which are not directly concerned with the
stipulated standards.
In the first chapter, the vibration standards established by the USBM for blasting,
quarrying, and construction activities were seen. Below are the standards established by
some of the other countries.
1. British Standards
The British standards provide guidance on the possibility of the damage due to the blast
vibrations and the guide values are set at the lowest vibrations levels above which credible
proof of damage has been established in their studies. The source of vibration considered
38
in establishing the standards are blasting, demolition, tunneling etc. The values in the
Figure 2-15, are vibration limits for the cosmetic damage which is the maximum value of
any of the three perpendicular components at any given time of the duration of the study.
Further, the figure details the transient vibration standards, if the case is of the continuous
vibrations which can give rise to resonant responses at lower frequencies, the velocity
levels are reduced by 50% than as shown in the Figure 2-18
Figure 2-18: Transient vibration guide values for the cosmetic damage BS 5228-2:2009
2. German Standards
The German Standards DIN 4150, Part 3, talks about the effects of construction vibrations
of both transient and continuous types. The different types of the vibrations are measured
at the different locations. The Figure 2-19, shows that long-term vibrations are independent
of the frequency. This is a frequency dependent guidance of the values of the velocity based
on the different types of buildings.
39
Figure 2-19: DIN-4150 (3) Vibration velocity levels for the evaluation of the short term
and long-term impact
3. Swiss Standards
Swiss standard SN 640312 was introduced in 1979 and takes continuous and transient
vibrations. The buildings are divided into various categories as shown in Figure 2-20.
40
Figure 2-20: Building categories, SN 640312
The two frequency ranges are fixed for the various recommended vibration velocities.
Figure 2-21: Frequency range for the various building types
4. Indian Standards
The Directorate General of Mines Safety (DGMS) has set the permissible limits of
vibrations, as detailed in the Table 2-2 that must be complied by the mines in India, to
continue their license to operate
41
Table 2-2: DGMS prescribed permissible limits for ground vibration in India
Type of Structures Dominant Frequency
<8 Hz 8-25 Hz >25 Hz
1. Building/structures not belongings to owner
1.1 Domestic houses/ structures 5 mm/s 10 mm/s 15 mm/s
1.2 Industrial building 10 mm/s 20 mm/s 25 mm/s
1.3 Objects of historical importance
& sensitive structures
2 mm/s 5 mm/s 10 mm/s
2. Buildings belonging to the owner with limited span of life
2.1 Domestic houses/structures 10 mm/s 15 mm/s 20 mm/s
2.2 Industrial Buildings 15 mm/s 25 mm/s 50 mm/s
The various vibrations standards set up by the countries across the world are widely spread
and have a large range of frequency for the similar velocity levels, which is difficult to
understand. Further, it can be observed the standards are for the structures and buildings
inhibited by the human beings and cannot be generalized for any structure like high-wall.
So, it appears that each structure under consideration and those which can be affected by
the vibrations causing a safety concern should be studied independently to estimate the
impact of vibrations.
42
3 Experiment
As discussed in the first chapter, high-wall related incidents are still prevalent and there is
no significant guideline directly stating this problem. To better understand these high-wall
behaviors under dynamic inputs, an experiment was designed. The aim of the experiment
was to observe the effects of blast vibrations and observe the safe levels of vibrations and
frequency to operate under given conditions.
3.1 Experiment Stages
The project was broadly divided into two stages, with each stage having different steps.
The first stage consists of collecting the field data and second stage comprised of assessing
that field data and develop working numerical models after calibrating them by simulating
the field conditions. The various steps of the experiment are as shown in the Figure 3-1.
Figure 3-1: Experimental setup process of the research
Once the calibrated numerical model is created in 3DEC, a parametric study is done in an
attempt to understand the effects of various parameters such as the height of the high-wall,
the angle of the slope and the amplitude of the vibrations and the natural frequency of the
high-wall.
Create a high-wall model in 3DEC with boundary conditions
Create a high-wall model in 3DEC with boundary conditions and calibrate the model
using the vibration data collected from the field
Input the wave in the model with variable frequencies and observe the displacements
at the crest of high-wall
Observe the effects of various parameters such as height, angle and amplitude of
vibrations on the natural frequency of the high-wall
Selection of the site, collection and assessment of the field data
43
3.1.1 Field data collection
The site understudy was Nally and Gibson, Georgetown Limestone Quarry located in
Georgetown Kentucky, where the underground excavation of limestone is done using drill
and blast. The high-wall, as shown in the Figure 3-2, along the ramp connecting the open
pit with the underground entry is studied as any adverse effect on the wall would be
damaging to the operations and safety of the mine.
Figure 3-2: High-wall under study at Nally & Gibson, Limestone Quarry, Georgetown,
Kentucky
The field data collection aims to gather day to day vibrations generated from underground
blasting operations and capture the locations of the points on high-wall at various time
during the period of study.
The field data collection was divided into two stages:
1. Setup seismographs in the field
2. Scan high-wall using Maptek I-Site 8800
44
3.1.1.1 Seismograph Setup
To monitor the vibrations affecting the high-wall, seismographs as shown in Figure 3-3,
were set up. The seismographs were set up to collect the vibration, frequency, amplitude
of the blast vibrations. The data collected by the seismographs is accessed remotely using
a modem used to transmit data.
Figure 3-3: Setting up seismograph in field for data collection
3.1.1.2 Site Scanning
The high-wall under study was scanned using Maptek I-Site 8800, as shown in Figure 3-4.
The scanner collects the current location of the points on the high-wall. The data collected
at multiple times can help to identify the points, if any, which have moved from there
baseline position. The scanner is set up in the field at multiple locations, usually three, to
cover the high-wall from all the angles. The scanner takes a 360° picture of the area and
then the picture is divided into multiple sections to scan as per instructed by the user.
Sections expected to be most affected due to blasting vibrations and sections far away are
scanned with high density, implying that more data points are collected by reflection for
the given area of the wall. The scanned data is stored in a portable hand handled controller,
which can be later exported for further processing using I-Site Studio.
45
Figure 3-4: Maptek I-Site 8800 Scanner used to scan high-wall in field
3.1.2 Data Processing
The data collected from the field is processed at the lab and is used to develop numerical
models for the predictions of movement of the high-wall from blasting vibrations. The data
collected is processed in three stages:
1. Generate a digitized scan of high-wall from the acquired scanner data using I-Site Studio
software
2. Import and assess the vibration data collected by seismograph using Seismograph Data
Analysis
3. Develop a numerical model in 3DEC
46
3.1.2.1 Scanner Data Processing
The data collected by scanning the high-wall in the field is imported from the hand-held
controller. The different scans which are represented by different colors are stitched
together to generate a model as shown in Figure 3-5, comprised of all the points collected
in the field. The stitched model can be used to generate surfaces which further could be
used as an input for further numerical modeling using 3DEC. In the present research, due
to time constraint, this was not utilized, but it can be a further course of the study for the
future work.
Figure 3-5: Model generated by I-Site software from scan data collected in field
3.1.2.2 Vibration Data assessment
The vibration data from the underground blasting operations is stored in the seismographs
installed at the site. The data is accessed using Seismograph Data Analysis software as
shown in Figure 3-6, the data collected is used as an input for the simulating a dynamic
model in 3DEC.
47
Figure 3-6: Vibration data accessed using Seismograph Data Analysis
3.1.3 Numerical Modeling
A numerical model was implemented in 3DEC, and for design, simplicity and considering
the blast vibration amplitudes, the model was assumed to be made of a single material with
elastic properties. Table 3-1, details the properties of limestone that were assigned to the
model after the calibration of the model.
Table 3-1: Properties of Limestone assigned in model
Properties of Limestone Values
Density 5.5 slugs/ft^3
Bulk Modulus 6e8 lbf/ft^2
Shear Modulus 2.4e8 lbf/ft^2
Initially, for the numerical simulation, a 100ft model was implemented, Figure 3-7 shows
the boundary conditions of the model and Figure 3-8 details a schematic diagram of the
model. For, the dynamic input, the velocity recorded from the field was converted to a
stress history using equation 3.1 and a viscous boundary at the bottom of the model was
used to avoid reflection of the outgoing stress wave back into the model.
48
𝜎 = 2(𝜌𝐶)𝑉 (3.1)
here,
𝜎 = applied shear stress
𝜌 = mass density
𝐶 = speed of s-wave propagation through medium
V = shear velocity
Figure 3-7: 3D model with boundary conditions for the numerical model in 3DEC
49
Figure 3-8: Schematic 2D diagram of a 100ft model for the analysis
3.2 Calibration of the Model
Before the use of 3DEC model for parametric studies, the model was calibrated using the
vibration data collected from the field in a surface mine operation. Figure 3-9, shows one
of the velocity record collected from the field. The properties of the rock material were
adjusted as detailed in Table 3-1, and as shown in Figure 3-10, the resulting Fast Fourier
Transformation (FFT) comparison between numerical output and field data gives a
reasonable correlation. The calibration was done taking a numerical simulation output on
the base of the floor across the toe of the high-wall as the real-time data was collected on
the floor of the wall around 20 feet away from the toe as shown in Figure 3-8.
Calibration
Point
50
Figure 3-9: Velocity record data collected in the field
Figure 3-10: Calibration of the model by using the field vibration data
3.3 Parametric Study
The parametric study was focused on the determining the effects of variations in geometric
parameters as detailed in Table 3-2, of high-wall and vibration parameters of a blast on the
Measured Field
Data
Numerical
Simulation
51
frequencies affecting the strain rate in the high-wall. The parameters considered for this
study were:
1. High-wall height
2. Slope angle of the high-wall
3. Amplitude of vibration on the high-wall
Table 3-2: Various parameters considered for the study and their variations
High-Wall Height Slope Angle Amplitude
100ft 90 degrees 1 in/s
200ft 65 degrees 3 in/s
300ft 45 degrees 5 in/s
400ft 30 degrees
500ft
For the parametric study, initially, the natural frequency of the calibrated 100ft 3DEC high-
wall model was established. To determine the natural frequency of the model, it was
decided to shake the model with a constant amplitude velocity vibration. For this purpose,
an artificial input sinusoidal wave was created as shown in Figure 3-11, where the shear
stress histories were generated using the Equation 3.1 and they were applied at the base of
the model. The model was shaken with a wide range of the frequencies from 5 Hz to 60 Hz
for the fixed velocity amplitude of 1 in/s. The boundary conditions and the properties of
the model were not changed and were kept the same as when the calibration of the model
was done.
52
Figure 3-11: An artificial ground vibration sine wave with a frequency of 5 Hz
53
3.3.1 Establishing the natural frequency of the 100ft model
The 100ft calibrated 3DEC model was shaken with a range of shear wave frequencies and
the x-displacement of the mid-point of the crest line was recorded against the applied stress
wave as shown in the Figure 3-12. The figure displays that the displacement
Input Shear Wave (lbf) Output Displacement at Crest (in)
Figure 3-12: Output Displacement at the crest on various Input Shear Wave Frequencies
10 Hz
20 Hz
30 Hz
38 Hz
50 Hz
54
Further, the following figures explain the behavior of the model at various input
frequencies. The points 4,5,6 in the figure refers to the point on the toe, mid and crest of
the high-wall.
1. Frequency 5 Hz
Figure 3-13: The X-displacement time history for the 5 Hz stress wave on 100ft model
Figure 3-14: The X-displacement contour for the 5 Hz stress wave on 100ft model
55
2. Frequency 20 Hz
Figure 3-15: The X-displacement time history for the 20 Hz stress wave on 100ft model
Figure 3-16: The X-displacement contour for the 20 Hz stress wave on 100ft model
56
3. Frequency 30 Hz
Figure 3-17: The X-displacement time history for the 30 Hz stress wave on 100ft model
Figure 3-18: The X-displacement contour for the 30 Hz stress wave on 100ft model
57
4. Frequency of 38 Hz
Figure 3-19: The X-displacement time history for the 30 Hz stress wave on 100ft model
Figure 3-20: The X-displacement contour for the 38 Hz stress wave on 100ft model
58
5. Frequency 50 Hz
Figure 3-21: The X-displacement time history for the 50 Hz stress wave on 100ft model
Figure 3-22: The X-displacement contour for the 50 Hz stress wave on 100ft model
59
6. Frequency 60 Hz
Figure 3-23: The X-displacement time history for the 60 Hz stress wave on 100ft model
Figure 3-24: The X-displacement contour for the 60 Hz stress wave on 100ft model
60
It was observed as shown in Figure 3-25 that for up to a certain frequency of 38 Hz the
displacement of the particle at the mid-point of the crest line kept on increasing but after
that on increasing the frequency of the input wave, the displacement declined steadily. This
nature of any structure is observed at the natural frequency, where the maximum
displacement is observed and displacement on both sides of that frequency is smaller than
the displacement at that natural frequency.
Figure 3-25: Displacement vs Frequency, with 38 Hz natural frequency of the 100ft high-
wall
3.3.2 Effect of height of the high-wall on natural frequency
Once the natural frequency of the 100ft model was established, the height of the high-wall
was varied from 100ft to 500ft, keeping all the other parameters and properties the same.
The modeling was done to determine the effect of height on the natural frequency of the
different models. The models were shaken with the same stress history as was in the
previous case of the 100ft model. The results of the variation are detailed in Table 3-3
below.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
5 10 15 16 17 20 22 25 30 35 38 40 45 50 55 0
Dis
pla
cem
ent
( 1
0-3
in)
Frequency (Hz)
Displacement vs Frequency
61
Table 3-3: Variation in Natural Frequency with Height of the High-wall
Height of the High-wall Natural Frequency
100ft 38 Hz
200ft 35 Hz
300ft 32 Hz
400ft 30 Hz
500ft 29 Hz
3.3.3 Effect of slope of the high-wall on natural frequency
Once the effect of variation of the height of the model was established the next parameter
that was considered for the study was the slope of the wall. In the case of variation in height
the slope of the wall was kept constant at 90 degrees. In this case, the height of the wall
was kept at 100ft and slope of the wall varied from practical values in the range of 90
degrees to 30 degrees. The data for the natural frequency for the slope of 90 degrees was
captured in the previous section, so the other data points were captured during this study.
The frequency of the stress wave for the study was varied from the range of 5 Hz to 60 Hz.
The sampling rate was increased in some cases to collect close in data figures.
1. Slope Angle 45 degrees
1. Frequency 20 Hz
Figure 3-26: The X-displacement time history for the 20 Hz stress wave on 100ft model
62
Figure 3-27: The X-displacement contour for the 20 Hz stress wave on 100ft model
2. Frequency 28
Figure 3-28: The X-displacement time history for the 28 Hz stress wave on 100ft model
63
Figure 3-29: The X-displacement contour for the 28 Hz stress wave on 100ft model
3. Frequency 44
Figure 3-30: The X-displacement time history for the 44 Hz stress wave on 100ft model
64
Figure 3-31: The X-displacement contour for the 44 Hz stress wave on 100ft model
4. Frequency 55
Figure 3-32: The X-displacement time history for the 55 Hz stress wave on 100ft model
65
Figure 3-33: The X-displacement contour for the 55 Hz stress wave on 100ft model
Similar data was collected for the slopes with 65 degrees and 30 degrees. In the variation
in the natural frequency of the high-wall with the slope as detailed in Table 3-4, it was
observed that the natural frequency shifts slightly towards the higher side as the slope
becomes flatter.
Table 3-4: Variation of the Natural Frequency of the high-wall with Slope angle
Slope of the 100ft High-wall Natural Frequency
90 degrees 38 Hz
65 degrees 42 Hz
45 degrees 44 Hz
30 degrees 46 Hz
3.3.4 Effect of the amplitude of the vibration on natural frequency of high-wall
The amplitude of the artificial wave used for the simulation of the models at various
frequency was kept at 1 in/s for the sake of simplifying the calculation process. But to see
if there is any effect on the natural frequency of a high-wall due to change in the amplitude
of the input stress wave. The calibrated models of the 100ft and 300ft while keeping all the
other parameters same were shaken with the increased amplitude of the 3 in/s and 5 in/s.
66
It was found that the displacement measured at all the three concerned points at the
different frequencies was increased by the similar factor as the increase in the amplitude of
the input stress wave. The results of the study are detailed in Table 3-5 below.
Table 3-5: Effect of change in amplitude on Natural Frequency of High-wall
Height of the High-wall Peak Amplitude of Velocity Natural Frequency
100ft
1 in/s
38 Hz 3 in/s
5 in/s
300ft
1 in/s
32 Hz 3 in/s
5 in/s
67
4 Results
The parametric study concentrated on the effects of the following factors on the natural
frequency of the high-wall:
1. High-wall height
2. Slope angle of the high-wall
3. Amplitude of vibration on the high-wall
1. Effect of Height on Natural Frequency
Based on the results of the 100ft model, the study was extended to understand and observe
the effect of changing heights on the behavior of the high-wall. As shown in the Figure 4-
1 it is observed that for the similar properties and the vibrations levels, the natural
frequency starts to shift gradually to lower frequency levels with the increase of the high
of the high-wall.
Figure 4-1: Line Graph between Natural Frequency and High-Wall Height
2. Effect of Slope of the wall on Natural Frequency
The slope of the high-wall left in the mine depends on the various parameters, like
economic viability, the stability of the overall pit-slope angle and others. As the part of the
parametric study, as shown in Figure 4-2, the slope of the 100ft, 300ft, 500ft models were
24
28
32
36
40
100 200 300 400 500
Nat
ura
l Fre
qu
ency
(H
z)
Height of the High-Wall (ft)
Natural Frequency vs High-Wall Height
68
varied to various angles to see the effect of changing slope on the natural frequency of the
high-wall. Table 4-1, details the results of this study on the 100ft high-wall. It was
observed, as the slope of the high-wall moved towards more flatter angles, the natural
frequency of the wall shifted to higher frequencies. Further, Figure 4-2 shows the variations
of the natural frequency with the slope of the high-wall for various heights under study.
Table 4-1: Effect of Slope angle on the Natural Frequency of the 100ft High-wall
Slope of the 100ft High-wall Natural Frequency
90 degrees 38 Hz
65 degrees 42 Hz
45 degrees 44 Hz
30 degrees 46 Hz
Figure 4-2: Variation of Natural Frequency with Slope of High-Wall for various heights
3. Effect of Increase in Amplitude of Vibration on Natural Frequency
All the vibrations standards across the countries include the amplitude of the vibration, as
one of the key parameters. As the part of this parametric study, the effects on the natural
frequency of the high-wall was observed due to the change in amplitude of the blast
vibration shaking the high-wall.
25
30
35
40
45
50
30 45 65 90Nat
ura
l Fre
qu
ency
(H
z)
Slope of the High-wall (degrees)
Natural Frequency vs Slope of Wall
Natural Frequency_100 ft Natural Frequncy_300 ft Natural Frequency_500 ft
69
Table 4-3, below shows that the changing amplitude of the vibration does not have any
effect on the natural frequency of a high-wall. However, it was noted that the amplitude of
the displacement of the particle for varying frequencies increased by the similar factor as
the vibration levels.
Table 4-3: Effect of change in amplitude on Natural Frequency of High-wall
Height of the High-wall Peak Amplitude of Velocity Natural Frequency
100ft
1 in/s
38 Hz 3 in/s
5 in/s
300ft
1 in/s
32 Hz 3 in/s
5 in/s
Figure 4-3, shows the effect change in displacement by corresponding factor of three but
no change in natural frequency.
Figure 4-3: Comparison of Displacement and Frequency with Amplitude of 1 in/s & 3 in/s
0
1
2
3
4
5
6
5 10 15 16 17 20 22 25 30 35 38 40 45 50 55 60
Dis
pla
cem
en
t (1
0-3
in)
Frequency (Hz)
Displacement vs Frequency
Peak Velocity Amplitude_1 in/s Peak Velocity Amplitude_3 in/s
70
5 Conclusions and Recommendations
Based on the outcomes of the parametric study done, it can be observed that the natural
frequency of the high-wall, varies with the geometry, more specifically with the height and
slope angle of the high-wall. It was observed that, while keeping all the properties same,
with the increase in the height, the natural frequency of the high-wall shifts gradually to
relatively lower frequencies. A trend of lower natural frequencies was noted for more
vertical slopes as compared to the higher once with flatter slopes. Another important
observation was that there is no effect of the change in amplitude of the blasting vibrations
on the natural frequency of the high-wall. However, a corresponding increase in the
displacement of the particles was noted.
The Z-curve given by USBM gives safe limits of peak particle velocity and frequency from
blasting vibrations for buildings. It shows that blasting vibrations at low frequency could
be more damaging than those at the higher frequency. However, unfortunately, they are
restricted to specific cases of household structures and do not throw light on the limits for
the high-walls, a permanent and crucial structure to the safety of a mine.
As the perception of the moving away from lower frequencies to higher frequencies goes
stronger for buildings of one story and houses. It is required that other types of structures
be considered like high-walls.
It can be understood that most of the mines cannot afford to take the time and resources
out to do the numerical modeling of their structures and design their blasts accordingly.
One of the most useful methods to estimate the ground resonant frequency is the use of
single blast hole detonation as an input and measure the frequency of the ground. This can
be a good starting point for the blasting engineers.
A fundamental step in the analysis of ground vibrations produced by blasting and its effects
on the stability of high-walls is first to determine the natural frequency of the high-wall
and make sure that, in the process of shifting to different frequencies, either higher or lower,
71
the shift should be away from the natural frequency so that safety of high-wall and miners
is not compromised.
5.1 Future Course of Action
The natural frequencies observed during this study were on the higher side as compared to
what is usually monitored or discovered in the field. One of the reasons for this observation
could be the use of intact rock for the modeling. In the future course of study, it would be
interesting to see what are the effects on the natural frequency, when the joints and other
discontinuities are introduced in the numerical model. The use of scanners like the Maptek
I-Site 8800 in conjunction with numerical modeling, could also be useful for understanding
the movement of the wall and monitor the changes during the lifetime of high-wall.
72
Appendix
A. Variation in the natural frequency with the height of high-wall
A1. Model: 300ft and 90 degrees
Figure A 1:The X-displacement time history for the 15 Hz stress wave on 300ft model
Figure A 2: The X-displacement contour for the 15 Hz stress wave on 300ft model
73
Figure A 3: The X-displacement time history for the 32 Hz stress wave on 300ft model
Figure A 4: The X-displacement contour for the 32 Hz stress wave on 300ft model
74
Figure A 5: The X-displacement time history for the 50 Hz stress wave on 300ft model
Figure A 6: The X-displacement contour for the 50 Hz stress wave on 300ft model
75
A2. Model: 500ft and 90 degrees
Figure A 7: The X-displacement time history for the 25 Hz stress wave on 500ft model
Figure A 8: The X-displacement contour for the 25 Hz stress wave on 500ft model
76
Figure A 9: The X-displacement time history for the 28 Hz stress wave on 500ft model
Figure A 10: The X-displacement contour for the 28 Hz stress wave on 500ft model
77
Figure A 11: The X-displacement time history for the 55 Hz stress wave on 500ft model
Figure A 12: The X-displacement contour for the 55 Hz stress wave on 500ft model
78
B. Variation in the natural frequency with the slope of high-wall
B1. Model: 100ft and 65 degrees
Figure B 1: The X-displacement time history for the 20 Hz stress wave on 100ft model
Figure B 2: The X-displacement contour for the 20 Hz stress wave on 100ft model
79
Figure B 3: The X-displacement time history for the 30 Hz stress wave on 100ft model
Figure B 4: The X-displacement contour for the 30 Hz stress wave on 100ft model
80
Figure B 5: The X-displacement time history for the 42 Hz stress wave on 100ft model
Figure B 6: The X-displacement contour for the 42 Hz stress wave on 100ft model
81
Figure B 7: The X-displacement time history for the 60 Hz stress wave on 100ft model
Figure B 8: The X-displacement contour for the 60 Hz stress wave on 100ft model
82
B2. Model: 100ft and 30 degrees
Figure B 9: The X-displacement time history for the 15 Hz stress wave on 100ft model
Figure B 10: The X-displacement contour for the 15 Hz stress wave on 100ft model
83
Figure B 11: The X-displacement time history for the 46 Hz stress wave on 100ft model
Figure B 12: The X-displacement contour for the 46 Hz stress wave on 100ft model
84
Figure B 13: The X-displacement time history for the 55 Hz stress wave on 100ft model
Figure B 14: The X-displacement contour for the 55 Hz stress wave on 100ft model
85
C. Variation in high-wall natural frequency with the amplitude of vibration
C1. Model: 100ft and 3 in/s Amplitude
Figure C 1: The X-displacement time history for the 20 Hz stress wave on 100ft model
Figure C 2: The X-displacement contour for the 20 Hz stress wave on 100ft model
86
Figure C 3: The X-displacement time history for the 40 Hz stress wave on 100ft model
Figure C 4: The X-displacement contour for the 40 Hz stress wave on 100ft model
87
Figure C 5: The X-displacement time history for the 50 Hz stress wave on 100ft model
Figure C 6: The X-displacement contour for the 50 Hz stress wave on 100ft model
88
C2. Model: 100ft and 5 in/s Amplitude
Figure C 7: The X-displacement time history for the 15 Hz stress wave on 100ft model
Figure C 8: The X-displacement contour for the 15 Hz stress wave on 100ft model
89
Figure C 9: The X-displacement time history for the 25 Hz stress wave on 100ft model
Figure C 10: The X-displacement contour for the 25 Hz stress wave on 100ft model
90
Figure C 11: The X-displacement time history for the 50 Hz stress wave on 100ft model
Figure C 12: The X-displacement contour for the 50 Hz stress wave on 100ft model
91
Bibliography
Ambraseys, N.N. and Menu J.M. (1998). Earthquake Induced Ground Displacements.
Journal of Earthquake Engineering 16, 985-1006.
Anderson, D.A., Ritter, A.P., Winzer, S.R. and Reil, J.W. (1985). A method for site specific
prediction and control of ground vibration from blasting. Proceedings of the First Mini-
Symposium on Explosives and Blasting Research, San Diego, CA, 28-43.
Anderson, D.A. (1992g). Blast Vibration Frequencies What do they mean? International
Society of Explosives Engineers.
Barla, G., Monacis, G., Perino, A. and Hatzor Y.H. (2010). Distinct element modelling in
static and dynamic conditions with application to an underground archaeological site. Rock
Mechanics and Rock Engineering 43, 877-890.
Christopherson, K.M. and Viterbo, V.C. (2011). Trim blasting designs in the Morenci
Mine. International Society of Explosives Engineers.
Crum, S.V., Siskind, D.E. and Eltschlager K. (1992). Blast Vibration Measurements at Far
Distances and Design Influences on Ground Vibrations. International Society of Explosives
Engineers, 167-179.
Crum, S.V. and Pierce, W.E. (1995). House Responses to Low Frequency Ground
Vibrations from Coal Mine Overburden Blasting: A Technical Update. Proceedings of
International Society of Explosives Engineers, 76-88.
Crum, S.V. and Siskind, D.E. (2000). Response of Structures to Low-Frequency ground
vibrations: A preliminary study. International Society of Explosives Engineers.
Damjanac, B., Varun and Lorig, L. (2013). Seismic Stability of Large Open Pit Slopes and
Pseudo-Static Analysis. Slope Stability, Australian Centre for Geomechanics, Perth, 1203-
1216.
Deng, X.F., Zhu, J.B., Chen, S.G. and Zhao, J. (2012). Some Fundamental Issues and
Verification of 3DEC in Modeling Wave Propagation in Jointed Rock Masses. Rock
Mechanics and Rock Engineering,45, 943-951.
92
Dowding, C.H. (1996). Construction Vibrations, Prentice Hall, 30-38.
Dunn, P. and Cocker, A. (1995). Pre-Splitting-Wall Control for Surface Coal Mines.
Proceedings Explo Conference, 299-305.
Fang, H.Y. (1976). Field Studies of Structural Response to Blasting Vibrations and
Environmental Effects. Leigh University.
Glass, C.E. (2000). The influence of seismic events on slope stability. Slope Stability in
Surface Mining, Society of Mining, Metallurgy and Exploration, 97-105.
Halatchev, R. and Gabeva, D. (2017). Probabilistic analysis of seismic impact on open pit
stability. International Journal of Mining, Reclamation and Environment, 31:3, 167-186.
Jiang, Q.H., Liu, X.H., Wei, W., et al. (2013). A new method for analyzing the stability of
Rock Wedges. International Journal of Rock Mechanics & Mining Sciences, 60, 413-422
Jiao, Y.Y., Zhang, X.L., Zhao, J. (2007). Viscous Boundary of DDA for Modeling Stress
Wave Propagation in Jointed Rock. International Journal of Rock Mechanics and Mining
Sciences, 44(7), 1070-1076.
Kramer, S.L. and Smith, M.W. (1997). Modified Newmark Model for Seismic
Displacements of Compliant Slopes. Journal of Geotechnical and Geoenvironmental
Engineering, 635-644.
Kuhlemeyer, R.L. and Lysmer, J. (1973). Finite element method accuracy for Wave
Propagation Problems. Journal of Soil Mechanics and Foundations Division, Proceedings
of the American Society of Civil Engineers, Vol.99, 421-427.
Lin, J.S. and Whitman, R. (1986). Earthquake Induced Displacements of Sliding Blocks.
Journal of Geotechnical Engineering, 44-59.
Liu, H. L., Fei, K., and Gao, Y.F. (2003). Time History Analysis Method of Slope Seismic
Stability. Rock and Soil Mechanics, 24 (4), 553-557.
Lysmer, J. and Kuhlemeyer, R.L. (1969). Finite Dynamic Model for Infinite Media.
Journal of the Engineering Mechanics Division, American Society of Civil Engineers,
Vol.95, 859-877.
93
Ni, W., Tang, H., Liu, X., Yong, R. and Zou, Z. (2013). Dynamic Stability Analysis of
Wedge in Rock Slope Based on Kinetic Vector Method. Journal of Earth Science, 25 (4),
749-756.
Pal, S., Kaynia, A.M., Bhasin, R.K., et.al., (2012). Earthquake Stability Analysis of Rock
Slopes: A Case Study. Rock Mechanics and Rock Engineering, 45 (2), 205-215.
Preece, D.S., Pilz, J. and Zavodni, Z.M. (2010). Peak Particle velocity versus gravitational
acceleration as a Stability Criterion for earth retaining walls subjected to production blast
vibrations. International Society of Explosives Engineers.
Pierce, W.E., Crum, S.V. and Siskind, D.E. (1996). Assessment of Low-Frequency Blast
Vibrations and Potential Impacts on Structures. Contract Research Report by the U.S.
Bureau of Mines for the office of Surface Mining, Reclamation and Enforcement, 22.
Sarma, S. (1979). Stability analysis of embankments and slopes. Journal of Geotechnical
Engineering Division, ASCE 105(12), 1511-1523.
Sharma, A., Pandey, S., Mishra, S. et al. (2013). Unlocking iron ore by controlling
environmental using electronic blasting systems. 7th Congress-European Federation of
Explosives Engineers.
Shiguo, X., Wenkai, F. and Jianjing, Z. (2010). Analysis of the effects of Slope Geometry
on the dynamic response of a near-field mountain from the Wenchuan Earthquake. Science
Press and Institute of Mountain Hazards and Environment, CAS and Springer, 353-360.
Shipley, S.A., Leistner, H.G. and Jones, R.E. (1967). Elastic Wave Propagation-A
comparison between Finite Element Predictions and Exact Solutions. Proceedings
International Symposium on Wave Propagation and Dynamic Properties of Earth
Materials, University of New Mexico Press, 509-519.
Siad, L. (2003). Seismic Stability Analysis of Fractured Rock Slopes by Yield Design
Theory. Soil Dynamics and Earthquake Engineering, 23(3), 203-212.
Singh, V.K. and Singh, D.P. (1995). Controlled blasting in an Open-pit Mine for improved
Slope Stability. Geotechnical and Geological Engineering, 51-57.
94
Siskind, D.E., Stagg, M.S, Kopp, J.W. and Dowding, C.H. (1980). Structure response and
damage produced by ground vibration from surface mine blasting. United States Bureau of
Mines RI 8507, 74.
Siskind, D.E., Stachura, V.J. and Nutting, M.J. (1987). Low-Frequency Vibrations
Produced by Surface Mining Blasting over Abandoned Underground Mines. United States
Bureau of Mines RI 9078.
Siskind, D.E. (1998). Ground Vibration effects on Structures. International Society of
Explosives Engineers.
Stianson, J.R., Fredlund, D.G., Chan, D. (2011). Three-dimensional slope stability based
on stresses from a stress-deformation analysis. Canadian Geotechnical Journal, 48, 891-
904.
Tose, S.J. (2011). A review of the design criteria and practical aspects of developing a
successful Pre-Split. International Symposium on Stability of Rock Slopes in Open Pit
Mining and Civil Engineering, 525-546.
White, T., Farnfield, R. and Kelly, M. (1993b). The effects of Surface Mine Blasting on
Buildings. Proceedings 4th International Symposium on Rock Fragmentation by Blasting,
105-111.
Vazquez, J.R. and Fernandez, E.G. (1986R). Progress in studying low frequency vibration
waves caused by blasting. International Society of Explosives Engineer, 72-80.
Yang, R., Whitaker, T. and Kirkpatrick, S. (2009). PPV Management and frequency
shifting in soft ground near high-walls to reduce blast damage. International Society of
Explosives Engineers.
Zdazinsky, C. (2016). Preserving High-wall Stability by Shifting the Dominant Blast
Vibration Frequency with Electronic Initiation. International Society of Explosives
Engineers.
Zhao, T., Sun, J., Zhang, B. and Li, C. (2011). Analysis of Slope Stability with Dynamic
Overloading from Earthquake. Journal of Earth Science, Vol.23, No.3, 285-296
95
VITA
Abhinav was born in the Jaipur City of the Rajasthan in India. He earned his Bachelors of
Technology degrees in Mining Engineering with first class honors from the Indian Institute
of Technology, Varanasi in 2010. He was then employed at the Orica-Mining Services,
where he worked for more than five years in various capacities. Before, embarking on his
journey with the Department of Mining Engineering with the University of Kentucky in
2015. He was working as Technical Services Lead, spearheading a team of engineers to
execute mining projects. During his career, both in academic and industrial settings he
published seven papers at national and international levels. In the department of Mining
Engineering, he worked as a graduate research assistant under Dr. Jhon Silva-Castro. He
expects to graduate with a Master of Science degrees in Mining Engineering in December
2017.